Yeah man, i've heard a lot of people have taken their phone's to Apple and gotten replacement really easily for the Home Button issue. In one case, someone told the Genius Bar associate and they didn't even check it, they just went in the back and grabbed him a new phone.

What are the chances I get to the Apple Store and they turn me away? Like I said, it works most of the time but there are clearly some cases where clicks don't register.

I'm just afraid I'm gonna get down there and they're going to test it and it'll work perfectly, lol.

Haha, 90% chance they'll give you a new phone free of charge. Make sure you go in when it's busy though , they'll want to get you out of the store asap due to other appointments. It's called "premature home button failure". It's listed in their warranty, and they actually cover it, I read on it. No signs of physical damage almost always lead to a new iphone free of charge.

I ended up being able to exchange mine tonight for the same reason (well, that and a funky smudge that suddenly started appearing on my photos despite having an immaculate lens...and it doesn't show up in Hipstamatic photos, which is the weirdest bit). I'd tried restoring first in case that solved either the home button or camera issues but never got it all the way through the restore, so I finally gave up and dragged it into the store as-is. The genius gave me no trouble at all about exchanging it, despite it being 6 days out of warranty. He did specify that it was a one-time exception, but the 90-day warranty on the one I got today should (hopefully) carry me through until iP5 launch.

Mine just started this too! I thought maybe some moisture got into it at the pool yesterday, but there was no water by the phone and it was on a table 6 feet away. It barely works at all, and this problem just came out of nowhere. I'm not sure what to do.

Turns out it is a very low tech problem that can be solved fairly simply:
Dust accumulates and may lodge some particle under the home button. Either take a can of pressurised air and blow it up the Dock-connector, or just stick a hoover up there. It works wonders!

I tried the canned air and that didn't seem to fix it. But then after hitting it kind of hard on a soft couch, pillow, or computer chair, with the dock connector facing downward, it now works like a champ!